About This Chapter
How it works:
- Identify the lessons in Glencoe Geometry's Reasoning and Proof chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the reasoning and proof topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, re-watch the videos until you've mastered the material or submit a question for one of our instructors.
Students will learn:
- Critical thinking and logic in math
- Propositions, truth tables and truth values
- Math conjunctions and disjunctions
- Conditional math statements
- Logical equivalence
- Inductive and deductive reasoning in geometry
- Postulates and properties of geometric figures
- Applications of direct proofs
- Line segment bisection and the midpoint theorem
- Geometric postulates and algebraic laws
- Geometric proofs
Glencoe Geometry is a registered trademark of McGraw-Hill Education, which is not affiliated with Study.com.
1. What Is Inductive Reasoning? - Examples & Definition
In this lesson, you will learn to define inductive reasoning. Following the lesson, you will have the opportunity to test your knowledge with a short quiz.
2. Critical Thinking and Logic in Mathematics
Logic has its own unique language and way of defining what is true and false. Watch this video lesson to learn how you can critically think in the language of logic while working with math.
3. Propositions, Truth Values and Truth Tables
Watch this video lesson and learn what truth values are and what a truth table looks like. Learn how to go from a proposition to its negation and how that affects the truth values and the truth tables.
4. Logical Math Connectors: Conjunctions and Disjunctions
Watch this video lesson to learn how to identify conjunctions and disjunctions. Also learn the connectors that are used with each. Learn how you can use them to make statements.
5. Using Venn Diagrams to Show Conjunctions & Disjunctions
Watch this video lesson to learn how you can use a Venn diagram to show conjunctions and disjunctions. You will see what a conjunction looks like and what a disjunction looks like in a Venn diagram.
6. Conditional Statements in Math
Sometimes, what is true in the mathematical world of logic is false in the real world. Check out this lesson to learn how to identify conditional statements and how you can differentiate between what is logically true and what is true in reality.
7. Logic Laws: Converse, Inverse, Contrapositive & Counterexample
Logical statements can be useful, but only if we are able to determine their validity. In this lesson, we'll look at the various forms of a logical statement and see how they relate to each other.
8. Biconditional Statement in Geometry: Definition & Examples
In this lesson, you'll learn how to define and recognize a biconditional statement. We'll review conditional statements and their converses and look at examples of each. We'll also discuss the criteria for writing biconditional statements.
9. Law of Detachment in Geometry: Definition & Examples
This lesson is about a fundamental logical argument type called the Law of Detachment. The definition is given, and examples of valid and invalid uses of it are provided.
10. Law of Syllogism in Geometry: Definition & Examples
This lesson will explain the law of syllogism and provide several examples showing when it can be used to reach a valid conclusion and when it cannot.
11. Inductive & Deductive Reasoning in Geometry: Definition & Uses
Watch this video lesson, and you will learn how important inductive and deductive reasoning is in the field of mathematics, especially when dealing with proofs in geometry. Learn how these two fundamental forms of reasoning give rise to formal theorems.
12. Properties and Postulates of Geometric Figures
In geometry, there are some basic postulates that are relied upon as the basis for other theorems. Watch this video to learn about the postulates that deal with points, lines, and planes.
13. Direct Proofs: Definition and Applications
In math, we can't explain that something is true just because. That's not enough. In this lesson, we'll learn to prove things using one of our most straightforward tools, the direct proof.
14. Line Segment Bisection & Midpoint Theorem: Geometric Construction
Watch this video lesson and you will learn how to bisect a line segment without measurements using just a compass and a straight edge. You'll also learn about the midpoint theorem, which lets you calculate the midpoint if you have the measurements.
15. Algebraic Laws and Geometric Postulates
Watch this video to learn about the basic algebraic laws that are also part of the basic geometric postulates that form the basis for the geometry that we know and study today.
16. Geometric Proofs: Definition and Format
Do you have something to prove? Can you explain why? In this lesson, we'll learn all about geometric proofs, including the parts that comprise a proof.
17. Algebraic Proofs: Format & Examples
Algebraic proofs are actually kind of cool. Watch this video lesson to see how an algebraic proof shows you the mathematical reasoning behind your algebraic solutions. Use this method to show your teachers why your answer is the right one.
18. Segment Addition Postulate: Definition & Examples
In this lesson, we will review the definition of the segment addition postulate. We will also look at examples to clearly illustrate how this concept works in the real-world.
19. Reflexive Property of Equality: Definition & Examples
After watching this video lesson, you will understand the reflexive property of equality. You will learn what the formula for this property looks like and how you can use it to help you solve problems.
20. Symmetric Property of Equality: Definition & Examples
Have you ever finished a math problem only to see that the teacher's answer was written backwards? Find out why your answer is correct in this lesson on the symmetric property of equality!
21. Transitive Property of Equality: Definition & Example
After watching this video lesson, you will understand how the transitive property of equality works when you have two equations that are equal to each other. Learn the formula for this property and how you can use it to help you solve problems.
22. Angle Addition Postulate: Definition & Examples
In this lesson, you will learn the definition of the Angle Addition Postulate. We will look at some examples so that you understand how this postulate works.
23. Proving Angle Relationships
In this lesson, you'll learn to prove angle relationships using properties of congruent, complementary, and supplementary angles. Learn the concepts and apply them on practice problems.
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Other chapters within the Glencoe Geometry: Online Textbook Help course
- Glencoe Geometry Chapter 1: Points, Lines, Planes, and Angles
- Glencoe Geometry Chapter 3: Parallel and Perpendicular Lines
- Glencoe Geometry Chapter 4: Congruent Triangles
- Glencoe Geometry Chapter 5: Relationships in Triangles
- Glencoe Geometry Chapter 6: Proportions and Similarity
- Glencoe Geometry Chapter 7: Right Triangles and Trigonometry
- Glencoe Geometry Chapter 8: Quadrilaterals
- Glencoe Geometry Chapter 9: Transformations
- Glencoe Geometry Chapter 10: Circles
- Glencoe Geometry Chapter 11: Area and Volume
- Glencoe Geometry Chapter 12: Surface Area
- Glencoe Geometry Chapter 13: Volume